Simplify Square Root of 93536

Here we will show you two methods that you can use to simplify the square root of 93536. In other words, we will show you how to find the square root of 93536 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√93536 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 93536 to simplify the square root of 93536. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 93536. The factors of 93536 are 1, 2, 4, 8, 16, 32, 37, 74, 79, 148, 158, 296, 316, 592, 632, 1184, 1264, 2528, 2923, 5846, 11692, 23384, 46768, and 93536. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 93536 divided by the greatest perfect square from the list of all factors of 93536. We determined above that the greatest perfect square from the list of all factors of 93536 is 16. Furthermore, 93536 divided by 16 is 5846, therefore B equals 5846.

Now we have A and B and can get our answer to 93536 in its simplest radical form as follows:

√93536 = A√B

√93536 = 4√5846

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 93536 to simplify the square root of 93536 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 93536 and then take the square root of that product. The prime factors that multiply together to make 93536 are 2 x 2 x 2 x 2 x 2 x 37 x 79. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 93536 by the number (A) squared. 4 squared is 16 and 93536 divided by 16 is 5846. Therefore, B equals 5846.

Once again we have A and B and can get our answer to 93536 in its simplest radical form as follows:

√93536 = A√B

√93536 = 4√5846

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